US President Donald Trump said Monday he is happy to meet with Iran's leaders "any time" and without preconditions, one week after tensions soared between Washington and Tehran.

"I would meet with Iran if they wanted to meet. I don't know if they are ready yet," Trump told a White House press conference with Italian Prime Minister Giuseppe Conte at his side.

"No preconditions," he added.

"They want to meet, I'll meet. Any time they want. Good for the country. Good for them. Good for us. And good for the world."

Trump's offer comes after a provocative warning a week ago from Iranian President Hassan Rouhani, who said the US should not "play with the lion's tail" and warned that any conflict with Iran would be the "mother of all wars."

Trump responded with an all-caps tirade on Twitter: "NEVER, EVER THREATEN THE UNITED STATES AGAIN OR YOU WILL SUFFER CONSEQUENCES THE LIKES OF WHICH FEW THROUGHOUT HISTORY HAVE EVER SUFFERED BEFORE."

"WE ARE NO LONGER A COUNTRY THAT WILL STAND FOR YOUR DEMENTED WORDS OF VIOLENCE & DEATH. BE CAUTIOUS!" he added.

The US is regularly suspected of backing the idea of regime change, but analysts read the tweets as simply a way for Trump to pivot after a week of dire headlines over his much-maligned summit with Russia's Vladimir Putin.

In May, Trump -- who has made Iran his public enemy number one -- announced the US withdrawal from what he called a "defective" multinational nuclear deal with Tehran, and moved to reinstate punishing sanctions.

The 2015 agreement came in response to fears that Iran was developing a nuclear bomb. Washington's European allies maintain their support for the deal and have vowed to stay in it, though their businesses fear US penalties.

"I ended the Iran deal. It was a ridiculous deal," Trump said.

"If we could work something out that's meaningful, not the waste of paper that the other deal was, I would certainly be willing to meet."

Trump said he and Conte had agreed that the "brutal regime in Iran must never be allowed to possess a nuclear weapon. Never."

"We encourage all nations to pressure Iran to end the full range of its malign activities," the US leader added.

- 'I believe in meeting' -

Trump has repeatedly shown a willingness to cast traditional diplomatic protocol aside and meet with leaders shunned by other administrations, including North Korean leader Kim Jong Un.

"I believe in meeting," Trump said.

"Speaking to other people, especially when you are talking about potentials of war and death, and famine and lots of other things, you meet."

On July 23, US Secretary of State Mike Pompeo said Washington was not afraid to sanction top-ranking leaders of the "nightmare" Iranian regime.

Pompeo also said that Washington wants all countries to reduce their imports of Iranian oil "as close to zero as possible" by November 4, or face American sanctions.